Animating appearing/extending strip with gaps
There are a few methods that you could use to achieve this, some simpler, some more flexible. The one that follows can give you results similar to what's shown in the video.

First create a curve object that roughly follows your desired path, bevel its corners so you get less distortion on tight curves. In this example I use the great Curve Fillet Tool addon from the Blender CG Cookie Market (it's a paid extension, but worth the price IMHO), you can also use the Simple Curves Addon or just do it manually if you prefer.



Now add a plane object, scale it lengthwise so it's narrowest side is placed along the curve length for better precision. Also scale the other direction to match the desired line thickness. Make sure you apply the scale before proceeding.

Add an Array modifier to you plane, and set it to Fit Curve and pick the previously created curve. Tick the Option Merge to join the arrayed planes.

Now add a Curve Modifier on top of it, set it to the same curve and it should distort it along the curve length. Make both the plane and the curve coincide at the same scene coordinate to avoid unwanted distortions.



Now the magic all comes from a Build Modifier, which will make the strip like effect progressively grow along the curve as desired. (Scrub the timeline to see the effect)



If you want more control, optionally apply the Array and Curve Modifier Modifiers only (leaving the Build Modifier live) if you later wish to manually adjust the shape of the strip, like different materials along the path, varying width, colors or add gaps, otherwise leave all modifiers live for a more flexible non destructive workflow.